Question
Convert 3 from radians to decimal degrees. Round to 1 decimal place if necessary. 3 radians
Ask by Greene Clark.
Mar 23,2025 00:45
Upstudy AI Solution
Tutor-Verified Answer
Answer
3 radians is approximately 171.9 degrees.
Solution
We start with the conversion formula:
\[
\text{degrees} = \text{radians} \times \frac{180}{\pi}
\]
Substituting \(3\) for the radians, we get:
\[
\text{degrees} = 3 \times \frac{180}{\pi} = \frac{540}{\pi}
\]
Now, calculating the numerical value:
\[
\frac{540}{\pi} \approx 171.9
\]
Thus, \(3\) radians is approximately \(171.9^\circ\).
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Simplify this solution The Deep Dive
To convert radians to degrees, you can use the formula: degrees = radians × (180/π). Therefore, 3 radians × (180/π) gives approximately 171.9 degrees. So, 3 radians \( \approx 171.9 \) degrees.
Now, don't forget that π (pi) is roughly 3.14159, which helps you see why this conversion can feel a bit magical! It’s like turning the language of circles into a more familiar form—angles you can visualize in everyday life.
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